At Microsoft Frontier in Paris with @satyanadella, Eiffel Tower in the backdrop. My takeaway so far: the model is the easy part. Context, harness, access and trust are where the real work is. #AI

The Church around the corner.

Just another Friday on Île de la Cité.

Update Sept 11, 2026: Today, CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled. claymath.org/news/navier-sto…

21/ Until someone answers that, we can't say what was actually won this month. Your turn: which problem goes on Millennium 2 — and what's your argument that a swarm of agents can't touch it? Bonus round: which of my seven falls first?

20/ Worse: a list designed to resist machines is a benchmark wearing a prize costume. It gets optimized against on day one. So maybe the successor isn't a list of conjectures at all. Maybe it's a criterion: What distinguishes a 166-page Lean certificate from math understanding?

19/ Now the honest limits. If seven problems fall in months, the prize format is dead, and a sequel is a category error. Clay's stated goal was to show the public that the frontier is open. A list that saturates in a year demonstrates the opposite.

18/ BQP ≠ BPP — why it resists An unconditional separation would imply P ≠ PSPACE — itself wide open, and harder than anything on the original list. You inherit complexity theory's deepest barrier as a prerequisite.

17/ BQP ≠ BPP What it is: Prove that quantum computers are genuinely more powerful than classical ones. Why it matters: We've built an industry on assuming it. It has never been proven.

16/ CH — why it resists The hard part is deciding what would count as an answer at all. Zero sensitivity to compute. You cannot brute-force a question about which axioms we ought to adopt.

15/ The Status of the Continuum Hypothesis What it is: Is there a size of infinity sitting between the counting numbers and the real numbers? Why it matters: Gödel and Cohen proved our axioms can't answer it. Woodin asks whether there's a right answer anyway.

14/ One-way functions — why it resists Same meta-complexity barriers as P vs NP, plus a harder demand: average-case hardness, not worst-case. Strictly less tractable than the problem everyone already calls intractable.

13/ Do One-Way Functions Exist? What it is: Functions that are easy to compute and infeasible to reverse. Locks without keys. Why it matters: All modern cryptography assumes they exist. It's strictly stronger than P ≠ NP — proving P ≠ NP would not save RSA.

12/ Standard Model QFT — why it resists Physics constrains what counts as the right answer. There's no formal oracle to confirm you built the right object. Only a community of physicists saying "yes, that's the thing we meant."

11/ Constructive QFT for the Standard Model What it is: Build the mathematics of the actual theory of particle physics, rigorously, in four dimensions. Why it matters: Yang-Mills was the warm-up. The full theory — matter, renormalization — is what physics actually runs on.

10/ Turbulence — why it resists The statement isn't well-posed yet. Someone has to decide what "turbulence" formally means before anything can be proved. That decision is the work. And it's exactly what a system optimized to close proofs won't do for you.

9/ A Rigorous Theory of Turbulence What it is: Derive the observed statistical laws of turbulent flow — Kolmogorov's scaling — from the Navier-Stokes equations themselves Why it matters: Turbulence is the last unsolved pbl of classical physics. We model it. We don't understand it

8/ Standard Conjectures — why it resists The expected deliverable is a conceptual framework, not a derivation. Search finds proofs inside an ontology. It does not invent the ontology.

7/ Grothendieck's Standard Conjectures What it is: The search for one universal shape-measuring theory sitting underneath all the ones we already have. Why it matters: Hodge was the symptom. This is the disease. Large parts of modern algebraic geometry are written assuming it.